Find the true discount (TD) on a bill of ₹2520 due 6 months hence at 10% per annum (simple interest).

Introduction / Context:
We directly compute the true discount for a known face value F, using the simple-interest discounting factor x = r * t. TD discounts the face value to its present worth by accounting for time and rate until maturity.

Given Data / Assumptions:

• F = ₹2520.
• t = 6 months = 0.5 year; r = 10% p.a.

Concept / Approach:
Let x = r * t = 0.10 * 0.5 = 0.05. Identities: PW = F / (1 + x); TD = F − PW = F * x / (1 + x). Substitute F and x.

Step-by-Step Solution:

Verification / Alternative check:
PW = 2520 − 120 = ₹2400. Recheck: PW = F / (1 + x) = 2520 / 1.05 = ₹2400, consistent.

Why Other Options Are Wrong:
₹80, ₹140, and ₹180 do not match the exact computation using x = 0.05.

Common Pitfalls:
Applying simple interest on PW instead of F when forming TD; forgetting to divide by (1 + x).

Final Answer:
Rs. 120